Biodiversity provides support for life, vital provisions, regulating services and has positive cultural impacts. It is therefore important to have accurate methods to measure biodiversity, in order to safeguard it when we discover it to be threatened. For practical reasons, biodiversity is usually measured at fine scales whereas diversity issues (e.g. conservation) interest regional or global scales. Moreover, biodiversity may change across spatial scales. It is therefore a key challenge to be able to translate local information on biodiversity into global patterns. Many databases give no information about the abundances of a species within an area, but only its occurrence in each of the surveyed plots. In this paper, we introduce an analytical framework (implemented in a ready‐to‐use R code) to infer species richness and abundances at large spatial scales in biodiversity‐rich ecosystems when species presence/absence information is available on various scattered samples (i.e. upscaling). This framework is based on the scale‐invariance property of the negative binomial. Our approach allows to infer and link within a unique framework important and well‐known biodiversity patterns of ecological theory, such as the species accumulation curve (SAC) and the relative species abundance (RSA) as well as a new emergent pattern, which is the relative species occupancy (RSO). Our estimates are robust and accurate, as confirmed by tests performed on both in silico‐generated and real forests. We demonstrate the accuracy of our predictions using data from two well‐studied forest stands. Moreover, we compared our results with other popular methods proposed in the literature to infer species richness from presence to absence data and we showed that our framework gives better estimates. It has thus important applications to biodiversity research and conservation practice.
4. Our estimates are robust and accurate, as confirmed by tests performed on both in silico-generated and real forests. We demonstrate the accuracy of our predictions using data from two well-studied forest stands. Moreover, we compared our results with other popular methods proposed in the literature to infer species richness from presence-absence data and we showed that our framework gives better estimates. It has thus important applications to biodiversity research and conservation practice.
We study a random walk on a point process given by an ordered array of points (ω k , k ∈ Z) on the real line. The distances ω k+1 − ω k are i.i.d. random variables in the domain of attraction of a β-stable law, with β ∈ (0, 1) ∪ (1, 2). The random walk has i.i.d. jumps such that the transition probabilities between ω k and ω depend on − k and are given by the distribution of a Z-valued random variable in the domain of attraction of an α-stable law, with α ∈ (0, 1) ∪ (1, 2). Since the defining variables, for both the random walk and the point process, are heavy-tailed, we speak of a Lévy flight on a Lévy random medium. For all combinations of the parameters α and β, we prove the annealed functional limit theorem for the suitably rescaled process, relative to the optimal Skorokhod topology in each case. When the limit process is not càdlàg, we prove convergence of the finite-dimensional distributions. When the limit process is deterministic, we also prove a limit theorem for the fluctuations, again relative to the optimal Skorokhod topology.
Big data require new techniques to handle the information they come with. Here we consider four datasets (email communication, Twitter posts, Wikipedia articles and Gutenberg books) and propose a novel statistical framework to predict global statistics from random samples. More precisely, we infer the number of senders, hashtags and words of the whole dataset and how their abundances (i.e. the popularity of a hashtag) change through scales from a small sample of sent emails per sender, posts per hashtag and word occurrences. Our approach is grounded on statistical ecology as we map inference of human activities into the unseen species problem in biodiversity. Our findings may have applications to resource management in emails, collective attention monitoring in Twitter and language learning process in word databases.
In recent years we have witnessed an explosion of data collected for different human dynamics, from email communication to social networks activities. Extract useful information from these huge data sets represents a major challenge. In the last decades, statistical regularities has been widely observed in human activities and various models have been proposed. Here we move from modeling to inference and propose a statistical framework capable to predict global features of human activities from local knowledge. We consider four data sets of human activities: email communication, Twitter posts, Wikipedia articles and Gutenberg books. From the statistics of local activities, such as sent emails per senders, post per hashtags and word occurrences collected in a small sample of the considered dataset, we infer global features, as the number of senders, hashtags and words at the global scale. Our estimates are robust and accurate with a small relative error. Moreover, we predict how abundance of a hashtag or of a word may change through scales. Thus, observing a small portion of tweets and the popularity of a given hashtag among them, we can estimate whether it will remain popular or not in the unseen part of the network. Our approach is grounded on statistical ecology as we discover inference of unseen human activity hallmarks can be mapped into the unseen species problem in biodiversity. Our findings may have applications to different areas, from resource management in emails to collective attention monitoring in Twitter and to language learning process in word databases.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.